# Thread: limit of f(x,y) as x,y -> (0,0)

1. ## limit of f(x,y) as x,y -> (0,0)

lim f(x,y) (x^4y^4)/(x^2 + y^4)^3
x,y go to (0,0)

this limit does not exist and to prove that you must take the limit using two different directions and I did one limit on the x-axis y=0 and the limit is 0. Now i must use the equation y=x^1/2 and i can't find the limit of this equation i keep on getting lim=1/2. can someone help me please?

2. Hello,
Originally Posted by hharalso
lim f(x,y) (x^4y^4)/(x^2 + y^4)^3
x,y go to (0,0)

this limit does not exist and to prove that you must take the limit using two different directions (and such that they are different) and I did one limit on the x-axis y=0 and the limit is 0. Now i must use the equation y=x^1/2 and i can't find the limit of this equation i keep on getting lim=1/2. can someone help me please?
Well, the first limit is 0 and the second limit is 1/2
.
So you've just proved that the limit doesn't exist !

3. Originally Posted by hharalso
lim f(x,y) (x^4y^4)/(x^2 + y^4)^3
x,y go to (0,0)

this limit does not exist and to prove that you must take the limit using two different directions and I did one limit on the x-axis y=0 and the limit is 0. Now i must use the equation y=x^1/2 and i can't find the limit of this equation i keep on getting lim=1/2. can someone help me please?
Are you sure that the limit is 1/2? It looks like 1/2^3 = 1/8 to me.